Relating Structural Phase Transitions to Mechanoluminescence:
The Case of the Ca
1−xSr
xAl
2Si
2O
8:1%Eu
2+,1%Pr
3+Anorthite
Ang Fenga,b, Simon Michelsa,b, Alfredo Lambertic, Wim Van Paepegemc, Philippe F. Smeta,b,∗
aLumiLab, Department of Solid State Sciences, Ghent University, Krijgslaan 281-S1, 9000 Gent, Belgium
bCenter of Nano- and BioPhotonics (NB Photonics), Ghent University, 9000 Gent, Belgium
cMechanics of Materials and Structures (MMS), Department of Materials, Textiles and Chemical Engineering (MaTCh), Ghent University, Tech Lane Ghent Science Park 46, 9052 Zwijnaarde, Belgium
Abstract
The phenomenon of mechanoluminescence (ML), where phosphors emit light when pressure is applied, is considered to be closely related to the crystallographic structure of those phosphors. In this work we unravel this connection for the anorthite solid solution Ca1−xSrxAl2Si2O8, which displays two important phase transitions as a function of strontium content x (denoted as xSr), i.e., the nearly second-order P¯1-I¯1 and the ferroelastic I¯1-I2c at ambient temperature and pressure. The spontaneous strains reveal that the ferroelastic transition takes place whenxSr∈(0.70,0.75), while other optical methods suggest that the second-order P¯1−I¯1 takes place whenxSr is around 0.4. The ML intensity reaches its maximum when the second order transition takes place and drops to zero when the phosphors undergo the ferroelastic transition. The first transition already brings significant changes to electron occupations at traps in this solid solution.
The structural phase transitions in the anorthite solid solutions are reflected in specific ML properties, such as the ML intensity and the load threshold. Further analysis suggests this is due to the structural change of the hosts and the trap properties (trap density and electron population function). Analysis of the ML dynamics may therefore serve as a useful tool to investigate phase transitions in ML phosphors.
Keywords: solid solution, phase transition, mechanoluminescence, thermoluminescence, defect
1. Introduction
Mechanoluminesence is the non-thermal emission of light due to mechanical stimulation applied to solid mate- rials [1]. ML in inorganic luminescent materials (or phos- phors) is particularly interesting because of the underly-
5
ing physics and the potential application as stress sensor [2], ML display [3], wearable ML textile [4], and smart skin [5]. While a few ML phosphors are based on tribo- electricity [6] or the movement of dislocations [7], many others, which are often persistent phosphors, are based on
10
the accelerated detrapping of previously trapped charges (usually electrons) due to mechanical stimulation. Natu- rally, the ML intensity and kinetics depend on the trap depth distribution, the resultant electron population func- tion and the trapping and detrapping mechanisms. Differ-
15
ent populations of electrons in traps can be achieved by different charging conditions, such as charging duration, wavelength and temperature, or by a delay between the end of charging and the start of the mechanical stimula- tion.
20
Usually, the fundamental properties of traps in ML phosphors vary from one host-dopant combination to an- other. Solid solutions serve as a valuable research tool due
∗Corresponding author
Email address: [email protected](Philippe F. Smet )
to their capability to induce continuous variation of struc- tural properties between the involved end-member com-
25
pounds, which can often be optically probed. For example, ML in the (Ba,Ca)TiO3:Pr3+ system is enhanced by the increase of electro-restriction near the solution limits [8, 9].
A reduction of trap density can enhance ML contrast, fa- cilitating stress visualization [10]. Chemical substitution
30
can also introduce possible phase transitions, among which second-order transitions exhibit interesting phenomenon near the transition point. There, the correlation length increases to infinity [11] which induces physical properties that are absent in their end-member compounds, such as
35
stiffening or softening of structure [12], huge enhancement of piezoelectricity [13], or anomalies of specific heat [14].
Moreover, textures and superstructure are often found in low symmetry phases, and often modulate their properties.
One particular case is the enhancement of piezoelectricity
40
in Pb(Mg1/3Nb2/3)O3-PbTiO3by engineering of the mor- photropic phase boundaries [15].
Abundant in the earth crust, anorthite CaAl2Si2O8be- longs to the feldspar family, which is characterized by a framework of ordered [AlO4]/[SiO4] tetrahedra with cations
45
stuffed in the cavities [16]. It displays a transition from P¯1 to I¯1 at ∼ 514 K (ambient pressure), with the I¯1 structure being the dynamical average of small P¯1 do- mains [17]. The strontium counterpart, SrAl2Si2O8, crys-
tallizes in a similar structure (I2c) with random Al3+/Si4+
50
occupation at tetrahedra sites. It transforms to I¯1 at elevated pressure [18] or via Ca2+ doping [19]. In the solid solution of Ca1−xSrxAl2Si2O8, the I¯1 phase differs from the calcium end-member (P¯1) by a splitting of the Ca2+site into two adjacent ones with fractional occupa-
55
tion, while it differentiates from the Sr end-member (I2c) by the ordering of tetrahedra and symmetry-breaking of the framework structure. The effect of cation substitu- tion is an increase of the cation polyhedral volume, which expands the unit cell, and the excitation of two tilting
60
modes of tetrahedra, which are responsible for the elas- ticity anisotropy that enables them to behave like layered silicates [20]. Although local centrosymmetry can be de- stroyed by doping, resulting in ML in some doped cen- trosymmetric niobates [21], the mechanical properties of
65
the anorthite host may be more fundamental. A variation of the ML intensity with the Sr2+content in this solid so- lution was observed in Eu2+ singly doped [22] and Eu2+- Dy3+codoped [23] phosphors, where ML intensity reached its peak at xSr = 0.40 and disappeared at xSr = 0.80.
70
However, neither the relationship between trap density, electron distribution function and the chemical composi- tion nor the ML kinetics have been investigated in detail so far. The effect of chemical substitution and the resultant phase transitions can be expectedly shown in the photolu-
75
minescence spectra, ML intensity and electron population at traps. Therefore, we investigated the effect of phase transitions on optical properties, namely, photolumines- cence, persistent luminescence, and mechanoluminescence in Ca1−xSrxAl2Si2O8: 1%Eu2+,1% Pr3+, since Pr3+ has
80
been shown to enhance the persistent luminescence in CaAl2Si2O8[24].
2. Experimental
2.1. Phosphor Synthesis
Ca1−xSrxAl2Si2O8: 1%Eu2+,1%Pr3+ phosphors were
85
prepared by a solid-state reaction method. Stoichiometric amounts of CaCO3(Alpha Aesar, 99.99%), SrCO3(Alpha Aesar, 99.99%), SiO2 (Alpha Aesar, 99.99%, amorphous), Eu2O3 (Alpha Aesar, 99.99%), Al2O3 (Fluka, 99.9%, 10 µm), and Pr6O11 (Alpha Aesar, 99.99%) were weighted,
90
mixed and ground in an agate mortar for 20 min. The mixed powders were pressed into a pellet (diameter 16 mm, thickness 2-3 mm) at a pressure of approximately 100 MPa for 3 min. Subsequently, the pellets were placed into a corundum crucible and transferred to a water-cooled
95
horizontal furnace, heated to 1350 ◦C at a rate of 5 ◦C · min−1, maintained at that temperature for 6 h, and cooled to 900 ◦C at a rate of 2.5 ◦C· min−1. Finally, they were cooled down to room temperature naturally. A constant flow (rate 0.16 liter·min−1) of N295%-H25% forming gas
100
was used in the entire process of heating and cooling. The solid pellets were crushed and ground for 30 min into fine powders before further characterization.
2.2. X-Ray Diffraction
All powder X-Ray diffraction measurements were car-
105
ried out on a Siemens D5000 diffractometer, which op- erated at 40 kV and 40 mA with Cu Kα radiation in the Bragg-Brentano geometry. The scanning range of 2θ was 10-120◦ with a step-size of 0.02◦ and the speed was 0.001◦/sec. The Rietveld refinement was carried out with
110
the FullProf Suite [25] software.
2.3. Optical Spectroscopy
Photoluminescence spectra were collected on an Ed- inburgh Instrument FLS920 spectrometer at room tem- perature. The wavelength step during the measurements
115
was 0.25 nm. All spurious spikes in the spectra were re- moved and then smoothed with the software SpectraGryph [26]. Afterglow spectra, together with the corresponding PL spectra, were measured at a Princeton Instruments ProEMR 1600 EMCCD camera and an Acton SP2300
120
monochromator. The phosphors were charged by UV light (360 nm) from a Xenon lamp for 2 mins before spectra were taken.
2.4. Afterglow Duration Test
The afterglow (AG) duration was measured with a cal-
125
ibrated photometer (ILT 1700, International Light Tech- nology) equipped with a photopic filter (YPM). Powders were weighted (0.3 g) and placed on an aluminum plate with a holder (diameter 16 mm, depth 1 mm), and illumi- nated by a Xenon lamp with 1000 lux for 10 min. Then,
130
the plate was transferred exactly underneath the photome- ter (at a distance of approximately 20 mm) in a dark box and kept until the luminescence fell below 2×10−2 mCd
·m−2. The afterglow duration is defined to be the time it takes for the afterglow to drop below the 0.32 mCd·m−2
135
threshold.
2.5. Thermoluminescence and Thermal Quenching Phosphor powders were pressed into small discs (diam- eter of 5 mm) and then placed on a heating stage in a vac- uum chamber. A normal thermoluminescence curve can
140
be acquired in the following way. After excitation with 370 nm light from a LED (60 mA) for 5 min, the discs were cooled down to −60 ◦C and then heated up to 225
◦C at a fixed rate of 0.5◦C·sec−1. To reveal the electron population function, theTm-Tstopmethod was adopted ac-
145
cording to Ref [27]. After the UV excitation, the phosphor was heated toTstop (rate of 0.5◦C·sec−1) and then imme- diately cooled down to a low temperature∼ −60◦C (rate 0.5 ◦C·sec−1), and finally heated up to 225 ◦C (rate 0.5
◦C·sec−1). The luminescence was detected by the ILT1700
150
photometer. For thermal quenching measurements, the phosphor was cooled/heated to a certain temperature T and then illuminated by a 370 nm LED (60 mA) for 60 sec, and then spectra were acquired using a Princeton In- struments ProEMR 1600 EMCCD camera and an Acton
155
SP2300 monochromator. Four spectra corresponding to
the time slot of ∼54-55 sec of the charging duration were averaged to calculate the PL emission intensity at the cor- responding charging temperature. The temperature was increased from −60◦C to 225 ◦C in steps of 5◦C. After
160
interpolating the relative PL intensity at each temperature by a cubic spline method, all TL profiles were corrected by the corresponding thermal quenching file.
2.6. ML Profiles Measurement
Coupon samples (length >120 mm, width 12.5 mm,
165
thickness 2.0 mm) for ML measurements were prepared by the resin transfer molding method [28]. Resin (EpikoteT M Resin MGS LR 135) and hardener (EpikoteT M Resin MGS LR 137) were taken in a 10:3 weight ratio and mixed with ML powders (weight ratio 3%). They were degassed for 2
170
minutes to remove the air bubbles. By using a vacuum, the mixture was infused through a mold and cured at room temperature for 24 h before post-curing at 85 ◦C for 15 h. Tensile experiments were carried out with an InstronR ElectroPulsT M E10000 instrument, which offers accurate
175
loading through either digital displacement or force. A normal ML profile can be obtained in the following way, as illustrated in Figure 1a. The coupon was charged with a UV lamp (6 W, centered at 365 nm) for 150 sec (Charging), then left at rest for a period (Delay) before a deformation
180
of 0.6 mm at a rate of 1.0 mm·sec−1, which was confirmed to remain in the linear range of deformation. The maxi- mum deformation, i.e. 0.6 mm, was attained for at least 280 sec (Relaxation), before unloading to zero linearly in 30 sec. The light emission was collected by a HamamatsuR
185
H10722-210 multiplier tube (PMT), whose control voltage was set to 0.515 V. A closed shutter was used to protect the PMT from strong illumination during charging, but it was opened manually when the charging ended (delay ∼ 0.1 sec), enabling the collection of luminescence. The voltage
190
signal from the PMT was synchronized with voltage signals for digital displacement and force. All these signals were sampled at a rate of 2048 Hz via a National InstrumentsR data acquisition unit (NI9234), together with a Compact- DAQ chassis (cDAQ-9174).
195
Several types of information can be extracted from the ML profiles, as illustrated in Figure 1b. Subtracting the corresponding AG from a ML profile, one can define the net ML, which can be roughly reckoned as the lumines- cence due to the load without the contribution of AG.
200
The maximum of the net ML is defined as MLPeak, which is often obtained when the load reaches its maximum. The relative strength of net ML to AG, i.e., net MLAG , starts from zero, and changes with time when the load is applied. The maximum of net MLAG is defined as ContrastML. The part
205
of ML from the MLPeak to the end of Relaxation is called ML tail, which can be normalized by MLPeak to have a normalized ML tail. The duration for the normalized ML tail to decay from its initial valueI0to 0.1I0is denoted as t0.1.
210
0
sec Delay Relaxation Unload Charging
open
on off
Load
Light
Shutter closed UV
Lamp
(a)
UV off Load start sec
ML tail net ML
0.0 AG 0.0
ML
(b)
Figure 1: (a)The experimental procedures to study the ML proper- ties include charging the phosphors with a UV lamp (centered at 365 nm) for 150 sec, waiting some time (Delay) before applying the load, keeping the maximum load for 280 sec (Relaxation) and unloading the sample (in 30 sec).(b)Information can be obtained by process- ing the ML (blue) profile, together with the corresponding AG (red) profile in the absence of pressure. The net ML is simply ML-AG, whose maximum is MLPeak. The ML tail is the part of net ML after it passes MLPeak. A normalized ML tail is a ML tail normalized by the MLPeak, whose maximum is denoted asI0. The ContrastMLis the maximum value of net MLAG .
3. Results and Discussion
3.1. The I¯1−I2c Transition Takes Place atxSr ∈(0.70,0.75) The solid-state reaction method yields anorthites at the intended compositions. Small amounts ofα-Al2O3 are present as impurities, as indicated in typical Rietveld re-
215
finement patterns and further confirmed by EDX measure- ments (Figure S1, Figure S2 and Table S1 in the electronic supplementary information (ESI)). The Rietveld refine- ments converged for all chemical compositions, reaching relatively small R values. For CaAl2Si2O8, one expects a
220
phase transition from P¯1 to I¯1 at 514 K (ambient pres- sure), and the transition temperature Tc decreases with increasing strontium substitution, reaching room temper- ature when xSr ∈ (0.40,0.50) for Ca1−xSrxAl2Si2O8 [17, 30]. This leads to a natural choice of the P¯1 structural
225
0.0 0.73 1.0 0
0.021 0.07
Spontaneous Strain
e6 |x-0.75|0.354
e4 |x-0.75|0.293
(a)
(b)
Figure 2: The spontaneous strains (a) e4 and e6 reduce to zero around xSr '0.75, and the cell volumes(b)increase at different rate before and afterxSr'0.73, together with two modes of tilting of tetrahedra (inset, from Ref [29]). This indicates that the phase transition takes place whenxSr'0.73.
model for cell parameter calculations when xSr ≤ 0.70, since the I¯1 structure is related to P¯1 by splitting of each Ca2+site into two adjacent ones with fractional occupan- cies [16, 31], which can often be interpreted as statistical- dynamic average of the P¯1 structure [17]. The substitu-
230
tion of calcium with strontium brings a phase transition at xSr ∈(0.70,0.75). All cell parameters experience a turn- around in this chemical range where the transition takes place (Table S2 in the ESI). Previous reports revealed that the I¯1-I2c transition in Ca1−xSrxAl2Si2O8is mainly ferroe-
235
lastic (second-order) in nature, with a deviation to triclinic [19]. In the framework of mean-field theory, the order pa- rameter Qo, active in I2c, is related to spontaneous strains in triclinic phases [19, 32],
e4= c·cosα
co·sinβo∗ +cosβo∗ sinβo∗cosγ e6=cosγ
(1)
240
where the asterisk∗ refers to the reciprocal space and the subscript oto the paraelastic state (reference state). The
corresponding parameters in the reference state can be cal- culated by extrapolation [32] (Table S2 and Figure S3 in ESI). A clear drop ofe4to zero nearxSr'0.75 (Figure 2a)
245
indicates the phase transition, although the critical point xc is somewhat lower than those reported elsewhere [19], i.e. [0.86,0.91]. This difference might be due to the rela- tively low sintering temperature and short sintering dura- tion of the syntheses [33], as compared to those reported
250
in literature, e.g. 1500 ◦C and 72 h [19]. The samples are very likely to have some disorder at the Al3+/Si4+
site, which tends to drive the transition point to the Ca- rich end member [34, 35]. The critical exponent for e4
(e4 ∼ Qo ∝ |x−xc|θ), θ, is 0.293, indicating that the
255
phase transition is a combination of triclinic (θ= 14) tran- sition and a second-order (θ = 12) one. The difference in scaling law between e4 ande6 with chemical composition also indicates the deviation from a simple second-order phase transition and this may be attributed to a second-
260
order parameter Qs that is coupled to Qo quadratically [19].
The increasing strontium content induces tilting of the tetrahedra but at a different rate before and after the phase transition atxSr '0.75. The rigidity of [AlO4] and [SiO4]
265
tetrahedra allows to characterize the structure of the anor- thite with only four permitted tilting modes of tetrahedra [20]. Here, the disorder of Al3+/Si4+ only plays a mi- nor role, while the incorporation of larger cations, such as Sr2+, has a larger impact on the framework. Only two of
270
these tilt systems, i.e., tilt2 and tilt3 (inset of Figure 2b), characterized by an increase in tilt angles, are indicative of the expansion of cell volume due to chemical substitution.
Thus, the tilts increase at a faster rate below the critical point than above the critical point (Figure 2b).
275
3.2. The Photoluminescence (PL) Spectra Reflect a Tran- sition at xSr '0.70
Analysis of the PL spectra can reveal structural changes in anorthites, as the electronic 4f65d1-4f7 transitions in Eu2+are dependent on the local coordination. For allxSr,
280
PL excitation spectra (Figure 3a) display two excitation bands, one peaking at 260-290 nm (band A), another at 310-350 nm (band B). The position and relative intensity of these bands evolve withxSr, and the effective excitation wave number,
285
¯ νex=
RI(νex)νexdνex
R I(νex)dνex (2) transforms atxSr '0.70 (Figure 3b). The corresponding emission spectra (Figure 4a) consist of asymmetric bands centered at 405 to 429 nm due to the 4f65d1-4f7 tran- sition of Eu2+. As the xSr increases, the wavelength at
290
the emission maximum, i.e., λem, decreases nonlinearly tillxSr '0.70 before stabilizing, while the corresponding full width at half maximum (FWHM) increases slightly for the (0.7,1.0) range after a similar nonlinear decrease
in the range of (0.0,0.70) (Figure 4b). Such nonlinear be-
295
havior can only be revealed by densely samplingxSr in the anorthite solid solutions, otherwise false conclusions may be obtained, e.g. in Ref [36].
267 294 335 /nm 400
0 0.5 1.0
Normalized Intensity
0 0.7 1 B
A
(a)
0 0.4 0.7 1
30.5 31 33.5 34.5
(b)
Figure 3: Normalized PL excitation spectra of Ca1−xSrxAl2Si2O8
(a), display two bands, i.e., band A (260-295 nm), and band B (300- 360 nm), and the effective excitation wave number(b)shows a trans- formation atxSr '0.70. The blue dashed lines serve as guides for the eyes.
Clearly, the revealed transition behavior of PL spectra is related to the structural phase transition and the as-
300
sociated changes in the chemical environment of dopants.
Compared with Ca2+, Sr2+ has a larger ionic radius [37]
and smaller electronegativity [38], leading to smaller cen- troid shifts [39] with increasing xSr. Besides, the magni- tude of crystal field splitting is roughly reciprocal to the
305
square of the averaged center-ligand distance of a cation polyhedron [40, 41, 42]. Therefore, a blue shift of λem
of the emission band is expected before xSr '0.75, after which λem stabilizes probably because of the high sym- metry of the I2c phase. Similarly, the average excitation
310
wavenumber also increases with increasingxSr and trans- forms at xSr '0.70 due to the ferroelastic transition. Al- though the FWHM is not in a straightforward relation to
365 404 428 /nm 650
0 0.5 1.0
Normalized Intensity
0 0.7 1
(a)
405 415 425
em/nm
0.0 0.35 0.7 1.0
47 55 68
FWHM/nm
(b)
Figure 4: The emission spectra of Ca1−xSrxAl2Si2O8 (a)are asym- metric bands;(b)the wavelength at emission maximumλemshows a blue shift and the corresponding full width at half maximum (FWHM) decreases with increasingxSr before the transition point atxSr'0.70. The blue lines serve as guides for the eyes.
the optical properties in anorthite, it again reflects a tran- sition aroundxSr '0.75, where the structural transition
315
takes place.
3.3. The afterglow (AG) also Reveals the Ferroelastic Phase Transition
The afterglow results from the detrapping of electrons that populate traps according to the electron population
320
functionn(Etrap, t) withEtrap being the trap depth. Af- terglow is observed at room temperature for the entire solid solution range for xSr ∈(0.0,1.0), while their spec- tra agree well with their corresponding PL spectra when xSr <0.40 but show additional emission at 470 - 600 nm
325
whenxSr ≥0.40 (Figure 5a). This is probably due to the distortion of cation sites, rendering possible preferential occupation of Eu2+ centers and energy transfer between them [43]. The distortion is severe when either the cation sites are partially occupied or the Al3+/Si4+ sites are dis-
330
ordered (randomly occupied), i.e., whenxSr ≥0.4.
1 2 Intensity
360
430 470
600 /nm
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
0.40 0.50 0.60 0.70 0.80 1.00
= 0.00 0.10 0.20 0.30
AG excitation
PL
(a)
1 10 103 Time/sec
10-2 0.1 1 10
AG/mCd m-2
0.0 0.7 1.0
0.8 0.96 1.1
0 0.7 1 0.32
(b)
0.0 0.65 1.0
10 102 103
AG duration sec
0 total AG 7
0
AG duration
0.0
= 0.15 1600
0.65
(c)
Figure 5: The AG spectra (blue, (a)) agree with the PL spectra (grey,(a)) whenxSr < 0.40, but differ from PL spectra by additional emission at 470-600 nm whenxSr≥0.40. The afterglow profiles follow Becquerel’s decay law(b), and the exponentsβvary slightly around 0.96 (the inset).The black horizontal line defines the afterglow intensity threshold 0.32 mCd·m−2. The AG duration(c), which is proportional to the corresponding total AG (the inset), decreases with increasingxSr by a power law, and shows a transition point aroundxSr '0.70.
The blue dashed lines serve as guides for the eyes.
The afterglow profiles obey Becquerel’s empirical law [44] (Figure 5b),
I(t) =I0·(1 +b·t)−β. (3) The power factorβ is almost constant asxSr varies, yield-
335
ing a mean value of 0.96 (the inset of Figure 5b). The afterglow duration (AG duration) is defined as the time needed for the afterglow to reach the threshold of 0.32 mCd·m−2(the black horizontal line in Figure 5b). A care- ful analysis reveals that the AG duration is proportional
340
to the total amount of afterglow intensity found by inte- grating AG to 2×10−2 mCd·m−2 (inset of Figure 5c), and thus it serves as a measure of afterglow. The AG duration as a function of xSr displays two straight lines in a log(AG duration)-xSr plot, showing a turning point
345
aroundxSr '0.70, where the I¯1-I2c phase transition takes place (Figure 5c).
Normally, it is quite hard to derive the mechanism of af- terglow only from the decay law since it depends on numer- ous assumptions and the associated mathematical tech-
350
niques. The decay function of afterglow can be regarded
as an isothermal release of electrons in traps of a previ- ously charged phosphors [45]. Consider a phosphor with one kind of emitting center (densitym(t)) and one kind of filled trap (densityn(t) =R∞
0 n(Etrap, t)dEtrap) where re-
355
combination of electrons with emitting center must be via the conduction band (electron densitync(t)). There might be fully filled thermally disconnected deep traps (density C) that do not participate in the luminescence processes.
The afterglow profile is given by [46]
360
I(t) =−dm
dt = m
m+γ·(N0−n(t))·ϕ(t) (4) whereN0is the total density of traps, andγ= σσretrap
recomb the ratio of the cross section of retrapping (σretrap) to the cross section of recombination (σrecomb). σretrap is assumed to be independent ofEtrap. The functionϕ(t) is actually an
365
integration of first-order detrapping processes for electrons in the traps, i.e.,
ϕ(t) = Z ∞
0
p(Etrap)n(Etrap, t)dEtrap (5)
where p(E) = s·exp(−Ektrap
BT ) is the detrapping rate co- efficient with s being the ’attempt-to-escape’ frequency,
370
kB the Boltzmann’s constant andT the absolute temper- ature. Any afterglow function isϕ(t) corrected by a time- dependent factor (m+γ·(Nm
0−n(t))), leading to a possibly complicated function. Assuming the traps share only one trap depth, Adirovitch [47] achieved a solution of Equation
375
(4) by taking m(t) ≈n(t) (C = 0, and nc n ), which yields,
p(Etrap)t= (1−γ)·log n0
n(t)
−γN0· 1
n(t)− 1 n0
(6) A map of γ to β in Becquerel’s decay law (Equation (3)) was constructed by numerical calculation. The value of
380
β = 0.96 means γ ∼100, which is 100 times higher than that of a second-order kinetics (γ= 1). This does not pro- vide a physical explanation of the afterglow decay. A sec- ond order process does not produce the right asymptotic decay law, whether the traps are considered as a distribu-
385
tion or not [48]. The presence of thermally disconnected deep traps in real materials results in the prevalence of near first order kinetics of thermoluminescence [49]. Note that the afterglow profiles for all the xSr follow the t−1 behavior asymptotically, which is a characteristic of a dis-
390
tribution of decay rate coefficients if first-order kinetics are assumed [50, 51]. Actually, the Becquerel decay law with β ∼ 1 can result from a distribution of rate coeffi- cients which is broad enough (for example Gaussian [52], exponential [53], Gamma [54], or even a uniform [53] dis-
395
tribution). Furthermore, the electron population function n(Etrap, t) can be evaluated from the distribution H(p) of the rate coefficient p for first-order afterglow. There- fore, the AG profiles of the anorthite solid solutions reveal relatively broad probability distributions of the rate coef-
400
ficients, and thus broad distributions of n(Etrap, t). This is confirmed in section 3.5 where the electron population function is discussed in detail.
3.4. Change in Mechanoluminescence Dynamics Before and After the P¯1-I¯1 Transition
405
While the afterglow is determined by the trap popula- tion and the thermally driven detrapping, ML is initiated by the application of pressure. Both phenomena are closely related, as for instance, the application of pressure shortly after ending the excitation will superpose the ML response
410
on the afterglow decay profile. On the other hand, the me- chanically driven detrapping also induces some retrapping at shallow traps, leading to a quickly decaying emission intensity after ending the application of pressure, the so- called ML tail.
415
The net ML responds linearly to the dynamic load after a threshold, which is dependent on the Delay time and also on the chemical compositionxSr. For example, the net ML for the xSr = 0.40 phosphor (Figure 6a) shows excellent linearity between the net ML and the load for all Delay
420
ranging from 2 to 610 sec, after a threshold, ranging from
0 1 2 Load/MPa 12.5
0 0.05 0.16 0.25 net ML/V
1 10 100
Delay 0.8
1.8Threshold/MPa
Delay/sec
1 10 610
sec
(a)
0.00 0.40 0.70
0 1.4 3.6
Threshold/MPa Delay/sec
2 20 700
(b)
Figure 6: (a) ForxSr = 0.4, the net ML increases linearly with load, after a threshold which increases with increasing Delay time investigated (the inset). (b)The threshold of net ML for allxSr∈ (0.0,0.70) is an increasing function of their corresponding Delay time.
The average threshold (indicated by the horizontal lines) increase with increasingxSr forxSr ∈(0.4,0.70). The vertical lines are the corresponding standard uncertainty.
0.8 to 1.8 MPa (the inset of Figure 6a). The threshold of ML for anyxSr ≤0.7 in anorthite, as shown in Figure 6b, increases as the Delay time increases. Meanwhile, the average threshold (indicated by the horizontal lines) stays
425
actually quite stable whenxSr≤0.40, and increases with xSr for higher strontium concentrations. This suggests a transition in the relation between the threshold and xSr
around xSr = 0.4, which coincides with the range where the P¯1-I¯1 transition takes place [55].
430
The ML peak intensities, MLPeak, decrease with in- creasing Delay time (Figure 7a), following the Becquerel law (Equation 3) withβ values around 0.78 (the inset of Figure 7a), which is nearly independent ofxSr in the solid solution. The ML disappears whenxSr >0.70, where the
435
ferroelectric structural phase transition takes place (see Figure 2a). We introduce t1
0.1 as the average decay rate function, where t0.1 is the duration that the intensity of the normalized ML tail takes to decay from I0 to 0.1I0.
Clearly, t1
0.1 also follows Becquerel’s law with Delay, with
440
β values around 1.0 (Figure 7b). It is noteworthy that the fitting curves for xSr ∈ (0.0,0.4) are very close to each other but are very distinct from those forxSr∈(0.5,0.7).
These two ranges may set the ranges for the P¯1−I¯1 phase transition in the anorthite solid solutions, although it was
445
not revealed in the structural studies. Furthermore, theβ values for xSr = 0.7 are high in both figures. This might be due to the closeness of the chemical composition to the critical transition pointxc, which is in the range (0.7,0.75).
1 10 100 Delay/sec
1 10 100
0 0.3 0.7
0.65 0.78 1 0.6 0.4
0.2
0.1 0.3
0.5
0.0
= 0.7
(a)
1 10 100 Delay/sec
10-2 0.1 1
0 0.7
0.7 1.0 1.3 0.20 0.50 0.40 0.60
0.70
0.30
= 0.00
0.10
(b)
Figure 7: The ML-Peak(a)and the average transition ratet1
0.1 (b) follow Becquerel’s decay law with Delay time, while their βvalues (in the corresponding inset) slightly depend on chemical composition, with mean values 0.78 and 1.0, respectively.
The Contrast of ML, ContrastML=max netMLAG , im-
450
proves with increasing Delay time in a power law fashion and can be fitted by a straight line in a log(ContrastML)- log(Delay) plot, as shown in Figure 8. Since ML acts as an enhanced luminescence on top of AG, ContrastML is important to the understanding of ML dynamics and also
455
for the visualization of stress distributions (see Ref [10] for example). ContrastMLis a function ofxSr, and reaches its maximum when xSr = 0.60 for all the Delay times in- vestigated. Interestingly, the ContrastML of xSr = 0.40
takes the second place, because of the strong MLPeak and
460
relatively low AG. These results suggest another way of in- creasing ContrastML due to the increase of ML in case of chemical substitution. This is quite different from the re- sults of Zhang et al [10], where both AG and ML decrease with increasing Sr2+in (Ca1−xSrx)2Nb2O7:Pr3+, resulting
465
in an improvement of ContrastML due to the reduction of trap concentration.
2 20 Delay/sec 700
0.01 0.1 0.5
0.2 0.1
0.6 0.3
0.5 0.7
0.4
= 0.0
Figure 8: The ContrastML (data: scattered points, fitting: lines) increases with Delay for allxSr in Ca1−xSrxAl2Si2O8, following a power law. It is also a function ofxSr, reaching the maximum when xSr= 0.6 for all the Delay investigated.
It is possible to understand the ML characteristics (in- tensities, thresholds and tail kinetics) on the basis of the detrapping of the electrons from the traps. The amount of
470
released electrons due to mechanical stimulation depends on the electron population function, and thus on the distri- bution ofpwhen first order kinetics are assumed. Through inverse Laplace transformation, the Becquerel’s decay law produces a Gamma distribution of rate coefficients [56],
475
which leads to the corresponding time-dependent rate co- efficients [57],
k(t) = 1
τ0+t/β (7)
whereτ0is the inverse of the ”ensemble” average ofk, i.e., τ0 = hki1 . Clearly, k(t) follows an inverse power law at
480
large time limit. A different Delay time is actually prob- ing the electron population function n(Etrap, t), which is a monotonously decreasing function of t, at a different time. Thus, the MLPeak also decays with increased De- lay time. As Delay time increases, the electron population
485
n(Etrap, t) drops and a higher threshold for ML is expected and observed, assuming the conversion of dynamic load to detrapped electrons only depends on the phosphor itself.
The evolution of average threshold with xSr clearly sug- gests that full ordering at both cations and tetrahedral
490
sites is favorable for small thresholds, while partial occu- pation of cation sites often leads to increased threshold.
Furthermore, the quantity t1
0.1 also arises from the accel- erated detrapping rate which is related tok(t), indicating a power law decay.
495
3.5. Electron Population Functions Evolve with xSr
The electron population functionn(Etrap, t), which shows how electrons populate traps of different trap depth, is sen- sitive to the nature of traps in phosphors. It determines the magnitude and decay profile of the afterglow, given the
500
value ofγ. In addition, it can even predict the kinetics of ML if the mechanically stimulated detrapping of electrons is already known.
The evolution in absolute magnitude of the afterglow intensity is in accordance with the trend of the TL peak
505
maxima, which corresponds to the number of electrons in traps that are thermally accessible near room temperature.
The magnitude of the TL peak maxima (Figure 9a) and their corresponding total TL (integrated up to 190◦C) de- crease with increasingxSr (Figure 9b top), indicating the
510
decrease of trapped electrons available in these phosphors.
This explains the drop of the total afterglow intensity with xSr. The trap depth Etrap was estimated from the tem- perature of the TL peak maxima, Tm, according to the Urbach relation [58],
515
Etrap(eV) =Tm(K)/c (8) where c is a constant that depends on the choice of s. In this case, we chooses= 109Hz and the constantc is 500.
Equation (8) only serves as an estimate of trap depth.
The initial rise method provides the trap depth, regard-
520
less of the kinetics involved, but it requires high quality data in the initial rise region (up to<15% of the TL peak maxima) [59] and it is not sensitive to small variation in Tm. Clearly, the trap depth first decreases tillxSr'0.70 and then increases slightly when xSr > 0.7 (Figure 9b
525
bottom). The variation is associated with the phase tran- sition in anorthite solid solutions. Interestingly, the trap depth as a function of xSr when xSr ≤0.70 displays two regions where the slope is quite different, and the transi- tion point is aroundxSr '0.30, which has a slightly larger
530
trap depth than expected. This may indicate the P¯1−I¯1 transition.
The electron population function becomes broader in the ranges of (0.0,0.4) and (0.5,1.0) with increasing xSr (Figure 10). These broad distributions guarantee the cor-
535
rect asymptotic behavior of afterglow, i.e.,I(t)∼t−βwith β '1. The electron population function n(t, Etrap, q) at Etrap depends on the time t and initial charging condi- tions q. In the interval of trap depth [Etrap, Etrap+dE], the number of electrons at timet is,
540
dn(t, Etrap, q) =N(Etrap)·f(t, Etrap, q)·dE (9) where N(Etrap) is the trap depth distribution and f(t, Etrap, q) is the filling function (0≤f ≤1) [60]. The filling function is the ratio of the number of filled traps to the total number of traps at Etrap, and its value is
545
limited due to low charging temperature, thermal detrap- ping, or even optically stimulated detrapping [61]. Thus, the trap depth distributionN(Etrap), which can be evalu- ated according to the method in Ref [62], does not provide
-40 0 50 Temperature /°C190 0
100 195
TL Intensity
0.70 0.80 1.00 0.50
= 0.00
0.60 0.40
0.30 0.20 0.10
(a)
0 1 2.7 total TL/104
0.0 0.3 0.7 1.0
0.621 0.667
(b)
Figure 9: The TL curves (a) of the anorthite series after charging at 20◦C, and the corresponding total TL intensity (integration to 190◦C) (b, top panel) decrease with increasingxSr while the trap depth (b, bottom panel)Etrapdecreases first toxSr= 0.7 and then increases slightly when xSr ∈ (0.7,1.0), indicating the transition point. Blue dashed lines serve as guides to the eyes.
enough information to determine n(t, Etrap, q). Instead,
550
theTm−Tstop method was adopted to meet the task [27].
A linear relationship between Tm and Tstop with a slope of'1 indicates the existence of a continuous distribution n(t, Etrap, q) (Figure S5 in the ESI). These Tm were con- verted into their correspondingEtrap according to Equa-
555
tion (8), and the area between the TL curves of two neigh- boringTmwas taken as a measure of electrons situated in the corresponding trap depth interval. Such a broad dis- tribution for shallow-intermediate traps can already lead to Becquerel’s decay law because its corresponding distri-
560
bution of rate coefficient is a Gamma function [56] that encompass both broad distribution (e.g., exponential dis- tribution) and narrow distribution (e.g., Gaussian distri- bution), resulting in a decay function similar to the Bec- querel’s decay law if the width of the distribution is broad
565
enough [52].
The probability density functions (pdf) ofn(Etrap, t, q) forxSr = 0.3 and 0.4 stand out as they display apprecia-
0.20
0.65
0.7
0.75
0.8
0.85
0.21 0.20 0.17 0.17 0.27 0.26 0.22 0.29 0.18
0.30 0.20
0.10 0.40 0.50 0.60 0.70 0.80 1.00
= 0.00 pdf
Figure 10: The normalized probability density function (pdf) ofn(Etrap, t) (att'0 sec) in anorthite solid solutions for variousxSr. The xSr= 0.3 and 0.4 phosphors show very flat population.
Structure 0.0
0.4
0.7
1.0
0.07 430durationAG 103 70 0.2Threshold5 0.7Total TL3 pdf 0.3
partial occup.
full occup.
tetrahedra disordered tetrahedra ordered
410 102 0.1 1
0 0.6
104 9
Delay:
45 sec
Delay:
45 sec
1
Figure 11: Both structural transitions, i.e., P¯1-I¯1 and I¯1-I2c transitions, are highly reflected in the ML properties and the electron population function. Meanwhile, the spontaneous strains, the PLλem, the AG duration and the total TL show a change corresponding to the I¯1-I2c transition atxSr∈(0.70,0.75). Two pairs of dash-dotted grey lines indicate the possible range of phase transitions.
ble states at intermediate-deep trap depth, resulting in very broad and flat distribution. Accidentally, this feature
570
takes place in the xSr range where P¯1-I¯1 occurs. Inter- estingly, the pdf of xSr = 0.7 is broader than those of xSr = 0.5 or 0.6. Apparently, the more Sr, the broader the distribution in each range. For the investigated 1-700 sec Delay time, the pdfs change their shallow traps greatly,
575
as the TL as a function of delay time after charging at 20
◦C forxSr = 0.0 and 0.10 shows only a shift of ∼20 K in Tm, corresponding to a shift of trap depth of ∼ 0.04 eV (see Figure S7 in the ESI). However, this does not exclude the participation of electrons at deep traps for ML.
580
3.6. The Structural Phase Transitions Are Reflected in Optical Properties
Putting all the results together in Figure 11, we can easily see that the ML properties are very sensitive to the P¯1-I¯1 phase transition, which is hardly reflected in sponta-
585
neous strains, PL spectra (e.g. ¯νex andλem), AG duration or total TL. Interestingly, the pdf of electron population is quite flat when xSr ∈(0.3,0.4). This shows strong ev-
idence that the defect chemistry of the anorthites has an important impact on their optical properties.
590
It is not possible to ascribe ML properties to the struc- tural defects directly, but certain speculations can be made at this moment. Normally, ML is believed to originate from the accelerated detrapping of electrons at traps due to the presence of an internal electric field near the defects
595
during dynamic loading [63]. This process heavily depends on the symmetry and mechanical properties of the host of ML phosphors [64]. Then, a disordered structure of cation polyhedra facilitates the detrapping of electrons because this disorder provides a wide range of states of electrons
600
suitable for the detrapping due to the creation of the inter- nal electric field, resulting in brighter ML. ML is extremely sensitive to the I¯1-I2c transition, while spontaneous strains, PLλem, AG duration, and TL properties only show a grad- ual change near the transition point. Therefore, ML seems
605
quite suitable for research of structural transitions in ML phosphors, especially near the transition point.
4. Conclusion
There are two important phase transitions in the anor- thite solid solution Ca1−xSrxAl2Si2O8:Eu2+,Pr3+, namely
610
P¯1-I¯1 atxSr '0.40 and I¯1-I2c atxSr'0.70. The occupa- tion of Al3+/Si4+at tetrahedral sites changes from ordered (xSr ∈ (0.0,0.70)) into disordered (xSr ∈ (0.70,1.00)), while the cation sites are partially occupied by Ca2+/Sr2+
(split-atom model) only in the range of xSr ∈(0.4,0.70).
615
The I¯1-I2c transition can be well deduced from spontaneous strains, PL spectra, AG duration, total TL intensities and also the presence of ML intensities. Meanwhile, the P¯1- I¯1 transition can only be reflected in the evolution of ML intensities, the ML thresholds, and average decay rate of
620
ML tail t0.1, as these quantities show a transition when xSr ' 0.4. In addition, the electron population func- tions are broad distributions, which leads to the correct afterglow profiles, and are sensitive to reveal both transi- tions. MLPeak andt0.1follow a power law decay with De-
625
lay time because of the accelerated detrapping of electrons from traps. Therefore, ML may serve as a very sensitive probe that allows to investigate structural transitions in ML phosphors.
Acknowledgment
630
This research was supported by the Special Research Fund (BOF) of Ghent University through the GOA project
“Enclose”. Simon Michels acknowledges the financial sup- port of FWO-Vlaanderen (SB grant 1S33317N). We thank Olivier Janssens for his assistance in measuring XRD of the
635
samples.
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